I have a specific question about random selection, representativeness and inference. It is well known that it's necessary to use random selection to get representative samples from the population of interest. But what happens with non-random samples?
I am working with an intentional sample. I compared the means of some of the main variables of my database with official data. And I can conclude that there aren't important differences between them. So I have a quite representative sample. However, I am confused about how to deal with this sample. When I estimate the means of some variables or the correlations between them, do I need to compute CI or p-values for this estimations?
I guess that it's not necessary, since I got the sample without random selection. Therefore, I have no sampling error, and I can't know how my estimations differ from the population. However, I have read some papers where the authors work with non-random samples and they make estimations (they use CI's and p-values). Moreover, it's difficult to use multivariate techniques (like ANOVA or regression) without the help of statistical significance.
Can anybody help me? I am very confused with this matter.